We present periodic calculations carried out with Gaussian-type basis sets on a test set of 21 solids with nine exchange-correlation functionals, extending previous works performed with two parameter-free correlation functionals (TCA and revTCA) which showed promising results for molecules in terms of key structural and energetic properties. Two LDAs and seven GGAs were considered for the prediction of equilibrium lattice constants, bulk moduli, and cohesive energies, using the same test set for all properties when possible. The effect of combining the TCA correlation with exchange potentials other than the PBE form originally used is also addressed. We find that the previously noted good accuracy of the parameter-free TCA functional for molecules also holds for solids, as long as a modified form of the exchange potential that is more biased towards solids than PBE is taken into account. In particular, the PBEsolTCA functional performs well overall for the three key structural and energetic properties considered here.